Hey can you please explain Fibonacci numbers in the simplest way possible because I really don't get them. Like i know the sequence goes 1,1,2,3,5,8,13,21, etc...But we have to fill in a table by plugging the numbers 1-9 in using the equation Fn+1. Please help me, Thanks
Of course! Fibonacci numbers are a sequence of numbers in which each number is the sum of the two preceding numbers. To understand how to fill in a table using the equation Fn+1, let's start with the first couple of Fibonacci numbers: 1 and 1.
1st Fibonacci Number: 1
2nd Fibonacci Number: 1
To find the next number in the sequence, we add the two preceding numbers together:
3rd Fibonacci Number: 1 + 1 = 2
So now we have the first three numbers in the Fibonacci sequence: 1, 1, 2.
To find the next number, we again add the two preceding numbers:
4th Fibonacci Number: 1 + 2 = 3
Now we have: 1, 1, 2, 3. And the pattern continues.
To make it easier to understand, let's create a table and use the equation Fn+1 to fill it in:
| n | Fn+1 |
|-------|---------|
| 1 | ? |
| 2 | ? |
| 3 | ? |
| 4 | ? |
| 5 | ? |
| 6 | ? |
| 7 | ? |
| 8 | ? |
| 9 | ? |
In the first row, we have the value of n, which represents the position of the Fibonacci number in the sequence. In the second row, we'll calculate Fn+1.
To calculate the values, we'll start with the first two Fibonacci numbers we know: 1 and 1.
For n = 1:
Fn+1 = F1+1 = F2
Since F1 is the first Fibonacci number, it is 1. So, F1+1 equals 1+1, which is 2.
So, in our table, we fill in the first row:
| n | Fn+1 |
|-------|---------|
| 1 | 2 |
For n = 2:
Fn+1 = F2+1 = F3
Since F2 is the second Fibonacci number, it is 1. So, F2+1 equals 1+1, which is 2.
Now our table looks like:
| n | Fn+1 |
|-------|---------|
| 1 | 2 |
| 2 | 2 |
For n = 3:
Fn+1 = F3+1 = F4
Since F3 is the third Fibonacci number, it is 2. So, F3+1 equals 2+1, which is 3.
Now our table is:
| n | Fn+1 |
|-------|---------|
| 1 | 2 |
| 2 | 2 |
| 3 | 3 |
We can continue this process to fill in the rest of the table for values of n from 4 to 9.
By following this method, you can fill in the table for any values of n and calculate the corresponding Fibonacci numbers using the equation Fn+1.